Final answer:
The direction of the electric field at (2.0 m, 2.0 m) with respect to the +x-direction is 45 degrees.
Step-by-step explanation:
The electric field direction can be determined by using the principle that electric field lines point away from positive charges and towards negative charges. In this case, there is a negative charge at the origin (0,0) and the position of interest is (2.0 m, 2.0 m). To find the direction of the electric field, we can draw a vector from the origin (0,0) to the position (2.0 m, 2.0 m). This vector points in the direction of the electric field with respect to the +x-direction. By considering the angle between this vector and the +x-direction, we can determine the direction of the electric field.
Using the trigonometric function tangent, we can find the angle:
tan(θ) = (2.0 m)/(2.0 m) = 1
Taking the inverse tangent of both sides:
θ = tan^(-1)(1)
Since tangent is positive in both the first and third quadrants, we can determine that the angle θ is 45 degrees. Therefore, the direction of the electric field with respect to the +x-direction is 45 degrees.